# Is the decay constant , constant for all isotopes of element

• CivilSigma
In summary, the question asks if the half life and decay constant are the same for every isotope, and the speaker believes it to be false based on intuition. They then discuss how to check this, mentioning the example of stable and unstable isotopes of hydrogen. The conversation concludes with the idea that the decay constant for hydrogen (with an infinite half-life) is not the same as for tritium (with a finite half-life), which shows how one can make conclusions from incomplete information.

#### CivilSigma

I have this true and false question:

" The half life and therefore the decay constant will be the same for every isotope
a) True
b) False
c) only if it is an isotope of the same element
"

I think this is false, just by intuition.

But you need more than just intuition... how could you check if all isotopes of the same element have the same decay constant?
For instance - can a stable element have radioactive isotopes?

Yes they can, I know there is Tritium , an unstable isotope of the stable element Hydrogen.

To check, we can place two samples in a container and monitor their loss of matter, and it should be equal?

Very good... so what is the decay constant for hydrogen?

I read that Tritium has half life of 13.2 years, where as deuterium has a halflife of 10.3 minutes. Thank you :)

Even if you didn't know those values, you know that tritium decays and hydrogen does not, so the decay constant for hydrogen (half-life infinity) is not the same as for tritium (half-life finite). This is how you can get needed conclusions from incomplete information.

CivilSigma

## 1. Is the decay constant the same for all isotopes of an element?

No, the decay constant is not the same for all isotopes of an element. The decay constant is specific to each isotope and is determined by the half-life of the isotope.

## 2. How is the decay constant calculated?

The decay constant is calculated by dividing the natural logarithm of 2 by the half-life of the isotope. This calculation gives the rate at which the isotope decays per unit of time.

## 3. Can the decay constant change over time?

No, the decay constant does not change over time. It is a constant value that remains the same for a given isotope. However, the amount of the isotope present will decrease over time due to radioactive decay.

## 4. Is the decay constant affected by external factors?

No, the decay constant is not affected by external factors such as temperature, pressure, or chemical reactions. It is an intrinsic property of the isotope and remains constant regardless of external conditions.

## 5. How does the decay constant relate to the concept of half-life?

The decay constant and half-life are inversely related. As the decay constant increases, the half-life decreases, and vice versa. This means that isotopes with a higher decay constant will decay at a faster rate and have a shorter half-life compared to isotopes with a lower decay constant.